This paper studies the iterative learning control (ILC) algorithm for first-order hyperbolic systems. Unlike most of the ILC literature of distributed parameter systems, in the iteration domain, that require identical desired trajectories. Here the desired trajectories are iteratively varying and described by a high-order internal model (HOIM). The HOIM-based P-type ILC design is firstly introduced in this paper to the first-order hyperbolic systems, which enable the systems to achieve the perfect tracking for the iteration-varying desired trajectories on $L^2$ space. Meanwhile, the convergence theorem of the proposed algorithm is established for first-order time-delay hyperbolic systems. Finally, simulation results testify the validity of the algorithm.

本文研究了一阶双曲系统的迭代学习控制（ILC）算法。与大多数 ILC 分布式参数系统文献不同，在迭代域中，需要相同的期望轨迹。在这里，所需的轨迹是迭代变化的，并由高阶内部模型 (HOIM) 描述。本文首次将基于HOIM的P型ILC设计引入一阶双曲系统，使系统能够完美地跟踪迭代变化的期望轨迹。${\mathrm{大号}}^2$空间。同时，针对一阶时滞双曲线系统，建立了所提算法的收敛定理。最后，仿真结果验证了算法的有效性。